In this section we give theoretical guarantees for the change-points estimated by optimal partitioning [1]}. This allows us to verify Assumption REF  for optimal partitioning in the case where we have sub-Gaussian noise. More precisely, we assume the setting of Section REF , with the exception that the condition
\(\limsup _{n \rightarrow \infty }\sigma / \underline{\sigma } < \infty \)  is not required. Similarly to Section REF , we denote the unknown set of true change-points by
\(\mathcal {T} := \lbrace 0 = \tau _0 < \tau _1 < \cdots < \tau _{K} < \tau _{K + 1} = n\rbrace .\) 
